IQ and university degree still works as a performance predictor in countries where free public university education is better (harder to get, gives more prestige) than private university education, so all the "good" students go to the best public universities (for example in my country - Poland).

There's still some inherited factors (who has better access to tutors at high school and who can move to a different city for 5 years without having to work). But at least you don't have to get a mortgage to afford a degree.

I think it's precisely because of recent communist history (in 1989 99% of population was equally as poor) that the private universities couldn't overtake the public ones. Not enough rich kids to make a whole university out of them - so instead the trick was to pass exams well enough to outcompete the other 49 candidates for a place at the best public universities.